We consider the problem of synthetic aperture radar (SAR) image formation, where the underlying scene is to be reconstructed from undersampled observed data. Sparsity-based methods for SAR imaging have employed overcomplete dictionaries to represent the magnitude of the complex-valued field sparsely. Selection of an appropriate dictionary with respect to the features of the particular type of underlying scene plays an important role in these methods. In this paper, we develop a new reconstruction method that is based on learning sparsifying dictionaries and using such learned dictionaries in the reconstruction process. Adaptive dictionaries learned from data have the potential to represent the magnitude of complex-valued field more effectively and hence have the potential to widen the applicability of sparsity-based radar imaging. We demonstrate the performance of the proposed method on both synthetic and real SAR images.